Manuscript XI-E@1 · XI-E.tex · section · 46e55514

The coordinate ghost-slot kernel

Route 2: localized support and the scalar-response frame › The coordinate ghost-slot kernel · lines 1106–1117

XI-E@1#eq:Wlocal

Put $a_{μ} = f \partial_{μ} ϕ$ and let $L_{ε}^{*}$ be the formal transpose into the metric slot. The complete first coefficient is

W_{f} (c; ϕ) = \int f (c /2 - L_{ε} R c) \cdot \partial ϕ d^{4} x = ⟨ a /2 - R^{*} L_{ε}^{*} a, c ⟩ .

Displayed formulas in this passage

XI-E@1#eq:Wlocal · line 1111
$W_{f} (c; ϕ) = \int f (c /2 - L_{ε} R c) \cdot \partial ϕ d^{4} x = ⟨ a /2 - R^{*} L_{ε}^{*} a, c ⟩ .$